Description

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures.
In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.show more

Review quote

Mancosu's scholarly book is very carefully researched, but it is also clearly written and fascinating to read. It is not to be missed by anyone with a serious interest in philosophy of mathematics. * Philosophia Mathematica * This is a very carefully researched and documented analysis of the rich relationship between philosophy of mathematics and mathematical practice during the 17th century. * Mathematical Reviews * Mancosu tells the story well and is good at bringing out significant points. * International Philosophical Quarterly * Mancosu's book shows philosophical acumen as well as high technical competence-and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading. * Isis * Students of the history of mathematics and philosophers of mathematics will find this a valuable addition to the literature. * Choice *show more

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